The union-closed sets conjecture is an elementary problem posed by Frankl in 1979. It goes like this: for any finite family of finite sets, closed under taking union, there exists an element that belongs to at least half of the sets in the family. This problem attracted recent interest for being a polymath project. I will explain important partial results and discuss a graph-theoretic reformulation of the conjecture. Based on joint work with Henning Bruhn, Jan-Arne Telle and Pierre Charbit.